Add gluten free flour, yeast, sugar, and salt to a large bowl. Whisk gently until everything is evenly mixed. This step helps the yeast spread well for a soft dough.

Pour warm milk into the bowl, then add the egg and melted butter. Stir slowly with a spatula until a sticky, smooth dough forms with no dry flour left.

Cover the bowl with a clean kitchen towel. Place it in a warm spot and let the dough rest for 30 minutes until it looks slightly puffed and smoother.

Place parchment paper on the counter and lightly dust with gluten free flour. Transfer the dough on top and gently roll it into a rectangle using a rolling pin.

Spread soft butter evenly over the dough. Mix brown sugar and cinnamon in a bowl, then sprinkle it evenly across the buttered surface for full flavor.

Carefully roll the dough tightly from the long side using the parchment paper as support. Cut into eight even rolls using a knife or dental floss.

Place the rolls into a lined baking dish with space between each one. Cover and let them rest for 15 minutes while the oven preheats.

Bake the rolls at 350°F for about 30 minutes until lightly golden and fragrant. Avoid overbaking to keep the rolls soft and tender.

Mix powdered sugar, milk, and vanilla until smooth. Drizzle glaze over warm rolls and allow it to melt into the cinnamon layers before serving.